Patterns Poster for Algebra 1

A month ago I wrote a post on First Day Lessons. Many — more than two — of you expressed interest in the lesson “Patterns Poster” for Algebra 1.

I would never redo a lesson if I didn’t think it was worthwhile, and I think this is the 7th year that I do this same lesson to start off algebra. So, if you’re still interested, this is the lesson in detail.

Why I love this lesson

It’s not tied to a specific unit/concept in the algebra curriculum, so you can do it whenever.

It’s visual.

Entry points are low — kids can draw the next step and the next. They can count the number of items in each step. They can see how the pattern is growing.

I suck at bulletin boards, so I decorate my classroom with students’ work. (By December, we’re looking up at the ceiling to see if we could showcase stuff up there.) These posters decorate the room quite nicely, and Back-to-School Night is just around the corner.

Kids are coming up with the equations themselves — this is powerful stuff!

Kids are talking with each other about their thinking.

First hour

I put this pattern up on the screen:

I ask students to sketch the 4th step in their math journal (quadrille-ruled composition notebook).

I ask them to sketch the 13th step.

I call on students to come up and share what they drew for steps 4 and 13.

We complete this T-chart together.

I ask them to write an equation for step n.

I give each student this patterns_poster. They notice that they just did all the steps with me, and now they get to go through the steps again with a different pattern. We go over both sides of the paper, including the rubric.

I interrupt them and say, “When I call out the pattern, raise your hand if you have that pattern, and I want you to look around the room to see who else has your same pattern because you’ll be helping each other after you work on it by yourself. Ready? Okay, raise your hand if you have pattern A…”

I add, “So when you think you have the equation, or when you are struggling with the pattern, I’m NOT the first one you come to. I’m gonna sit at my desk and paint my nails. You need to seek each other out first for help. Got that? Good!”

… OMG, I swear this lesson gets better and better each year. All 34 kids are working quietly on their patterns. Erica furrows her eyebrows, thinking hard. Janie kicks her backpack. Mike is talking to himself about how he sees the pattern growing. Doug is… WHAT?!! Doug is not misbehaving?! (I haven’t taught Doug before but his reputation precedes him.) He is completely into the pattern, carefully sketching the next steps.

The talk among them begins. They scoot their chairs closer. They find each other and form small groups. A few hands go up. I respond, “Do you need help? Have you talked with your pattern-mate yet?” The hands come back down. One student, “I haven’t yet. But I just want to clarify something.”

I’m now working with Chris. He has this pattern:

His sketch of the 13th step looks like this:

At the bottom of his paper, I see he has this expression for the pattern:

Our conversation goes something like this:

Me: Okay. Show me why the “plus 4” in the expression?

Chris: Hmmmm. The equation works.

M: I didn’t say it wouldn’t work. I just want to see where “plus 4” is in your sketch. Let’s take a look at your sketch for step 13 here. How did you get “4n + 4” from the drawing?

About five minutes later, I return to Chris’s desk, “How are you doing?” He says, “The ‘plus 4’ is the 4 corners.” Yes!!!! So as I talk with him, he realizes that these two sketches jive more with “4n + 4,” and he’s able to verbalize that whatever step number you’re on, there’ll be four groups of it around the square, and the “plus 4” is for the 4 corners.

We go back to his original sketch of step 13 and come up with a general sketch.

And he is able to write an expression that would represent these sketches better:

Then I ask, “Well, are these two expressions the same?” Chris looks at me like I need a refresher course on how to distribute.

Three kids have been patiently waiting for me to help them with this pattern below. One says, “We are really struggling, Mrs. Nguyen. I know you want us to struggle and all, but how much longer?” I laugh. I start helping them look at the pattern as sets of triangles, or they can start by focusing on the horizontal toothpicks only, then look at the ones that slope upward, downward, or maybe just the toothpicks along the perimeter… I say to them, “You have a tougher pattern here! Aren’t you lucky!”

They do not get the poster paper until I approve the work on the paper. I show them a few examples from previous years. (I’ve tweaked this assignment a little, so the requirements are not always the same from year to year. I wish I left in the rubric a written explanation of how they see the pattern like you see in the paragraphs on these posters.)

They’ll get one more class period to work on this for a total of three. I don’t believe in giving kids math class time to color and make things look pretty. (Large posters of tessellations make me cringe.) I just want what’s on the rubric, but for whatever reason the girls tend to spend more time — at home — making theirs very colorful.

Why not make the answer key yourself? Then you can write out some pocket questions with your answer key to help and assist students in creating the equations.

I use a weekly lifeline and I want to print out these patterns, cut them up, and copy them on so each day you have a warmup question that is drawing next 2 figures, equation, and challenge for the 43rd or whatever.

Thanks Fawn for this awesome resource!! Talk about number / math talks resource!!

Could you also send me the answer key to your website visualpatterns.org? The answer key will really help me have the confidence to try this in my classroom! These sounds great! Thank you!!!
– Kimberly

Your patterns are fantastic. I will have students work on them in visibly random groups to get them reasoning with each other. If you use vertical surfaces like whiteboards, windows, chalk boards then they can’t hide. Give them one erasable marker that they rotate, to add accountability. Since the surfaces are erasable, students will be willing to risk and won’t hesitate in case they are wrong. I’d still do the aspects of formative assessment chats like you describe in your sample lessons. I would also have them visit other groups to mobilize their data and build their understanding more deeply just as you describe. Here is a link to the research on this idea: [ http://www.peterliljedahl.com/wp-content/uploads/Visibly-Random-Groups.pdf ]http://www.peterliljedahl.com/wp-content/uploads/Visibly-Random-Groups.pdf
Thank you again for your valuable resource.

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I have been teaching for over 20 years and have been working really hard this year to revamp my teaching by using the many resources on the Internet. I came across your patterns poster activity as well as your website. I love it! I plan on using these this week. Thank you so much for the time and energy you put into creating it.

I’ve been working my way through the patterns as I find it makes helping the students easier. However, an answer key would still be useful. I tried the dropbox link and wasn’t able to access it. Was it removed and would it be possible to get it?

This is an AWESOME resource, thanks a million!
I am also looking for the answer key (equations) for these patterns. Tried the dropbox route but the link isn’t working for whatever reason. Can anyone help me out?

The previous president of NCTM recommended this type of activity last week to use on the first days of shcool so I went searching and found your post… What a great resource.. And thanks for the key– its not as easy as it seems–some really higher level ones here.
I love it! putting 2016-2017 plans together and this is #1
Thanks

[…] such an emphasis on functions in both of the courses I teach, I think this is the year to introduce Fawn Nguyen’s Visual Patterns. I keep reading hither and yon about effective uses of these patterns, and […]

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